Shape dependence of superconformal defects

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The shape deformation of conformal defects is implemented by the displacement operator. In this talk we consider superconformal defects and we provide evidence of a general relation between the two-point function of the displacement and the one-point function of the stress tensor operator. We then discuss the available techniques for the computation of this one-point function. First, we show how it can be related to a deformation of the background geometry. Then we conclude with a discussion of surface defects in four-dimensional N=2 theories, where the chiral algebra provides an additional powerful tool.